Two young Saudi women whose bodies were found a week ago along the rocky Manhattan shore of the Hudson River, bound together with duct tape around their waist and ankles, likely committed suicide, NY police said on Friday.

"We have them staying at a number of high-end hotels in New York City during this time", Shea said.

A passerby who frequently exercised in Riverside Park said he was jogging for his daily exercise routine Monday morning and witnessed two girls sitting together with their hands in their heads, loudly praying near the scene where they were found later that day.

He added that detectives were told by sources that the sisters said they would rather die than return to Saudi Arabia.

It's unclear what mode of transportation the sisters used and the specific time frames they visited each city, a NY police spokesman said.

The mysterious deaths of the Farea sisters have drawn worldwide attention and fuelled rampant speculation and online conspiracy theories in the wake of the killing of journalist Jamal Khashoggi at a Saudi embassy in Turkey.

Two women were found next to the Hudson River on the Upper West Side of the Manhattan borough of New York City on October 24.

The sisters were living until the summer in Fairfax, Virginia, although their mother had not seen them since they went missing from home in the city last December.

The tape that was found around the women's bodies gave rise to speculation, but Shea said it was not so much as "binding" the women together but rather "keeping them together".

As puzzled investigators search for answers, they are getting a clearer picture of where the sisters traveled before their deaths.

Rotana was formerly a student enrolled at George Mason University, according to school spokesman Michael Sandler.

Officials confirmed that at some point the sisters had applied for asylum in the U.S., referencing their alleged abuse.

On October 23, one day before their death, their mother claims that she received a call from the Saudi consulate ordering the family to return home.

The sisters were last seen in Fairfax on August 24.

Those allegations have not been corroborated, but they do make it unclear who would have reported the girls missing on September 12 in Fairfax.

"When the complete investigation is done, we'll have a good idea of what exactly transpired", NYPD Chief of Detectives Dermot Shea said earlier this week. At the time, police said the sisters were referred to county family services.

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